Geothermometry of calcite spar at 10–50 °C

Carbonate geothermometry is a fundamental tool for quantitative assessment of the geothermal and geochemical evolution of diagenetic and hydrothermal systems, but it remains difficult to obtain accurate and precise formation temperatures of low-temperature calcite samples (below ~ 40 to 60 °C). Here, we apply three geothermometry methods (∆47-thermometry, nucleation-assisted fluid inclusion microthermometry—hereafter NA-FIM—and oxygen isotope thermometry) to slow-growing subaqueous calcite spar samples to cross-validate these methods down to 10 °C. Temperatures derived by NA-FIM and Δ47-thermometry agree within the 95% confidence interval, except for one sample. Regression analyses suggest that the real uncertainty of ∆47-thermometry exceeds the 1 SE analytical uncertainty and is around ± 6.6 °C for calcite spar that formed at 10–50 °C. The application of δ18O thermometry was limited to a few samples that contained sufficient primary fluid inclusions. It yielded broadly consistent results for two samples with two other geothermometers, and showed higher temperature for the third spar. We also found that calcite with steep rhombohedral morphologies is characteristic of low temperatures (11–13 °C), whereas blunt rhombohedra prevail in the 10–29 °C domain, and the scalenohedral habit dominates > 30 °C. This suggests that the calcite crystal morphology can be used to qualitatively distinguish between low- and higher-temperature calcite.


Study design and sample selection
We used NA-FIM as the primary method for comparison with ∆ 47 -thermometry and OIT-derived temperatures obtained on the same samples.This decision was based on the fact that FIM (including NA-FIM) has an internal 'data quality check' that allows the reliability of the results to be evaluated based on the temperature variation obtained on individual FI assemblages (FIAs; groups of petrographically associated FIs that were likely entrapped at the same time).The currently accepted criterion is that 90% of the T h obtained from a FIA should fall within a 10 °C interval 7 .
To minimize potential biases due to isotopic disequilibrium that may affects OIT and ∆ 47 -thermometry, all measurements were made on coarsely-crystalline euhedral calcite crystals (spar) that formed in subaqueous environments and at very likely very slow growth rates (e.g. 18and Sample selection in the Supplementary Information).Samples of this study were collected from caves, vugs and veins in carbonate rocks in Hungary, Austria, France, and Kyrgyzstan (Table S1).Only occurrences lacking evidence of weathering and direct exposure to elevated temperatures at the surface were sampled.
FI petrography was performed on all samples (Supplementary Information, Fig S1).Well-defined primary FIAs were identified in 11 calcite spars, which were retained for further analyses (Table S2).On all these samples, formation temperatures were determined by NA-FIM and ∆ 47 -thermometry.OIT could be applied only on three samples that contained sufficient primary and only few secondary FIs.
Stable isotope analyses of calcite (δ 18 O c and δ 13 C c ) along the crystal growth axis were performed to provide a semi-quantitative assessment of possible temperature variations and/or changes in the isotopic composition of the paleowater during crystal growth.

Results
Temperatures obtained by the different methods on the same samples are summarized in Table 1.

NA-FIM
Mean values of surface tension-corrected homogenization temperatures (T h∞ ) 10 obtained from primary, initially single-phase liquid inclusions range from 11 to 41 °C (Table 1).Between 10 and 19 inclusions per sample were analyzed.Variations of T h∞ values within individual FIAs and across different FIAs in the same samples were mostly well below 10 °C (between 1.4 and 8.8 °C, Fig. 1), with standard errors (1 SE) ranging between 0.5 and 1.6 °C.The results demonstrate the high precision that can be achieved with NA-FIM.Ice melt temperatures indicate that the salinity of the FIs are between 0.5 to 0.9 wt.% NaCl equivalent (Table S3).

C c )
The Δ 47 measurements were performed on calcite powders drilled at the same locations on the crystals where the NA-FIM data were obtained.Δ 47 values range from 0.639 to 0.546‰ (relative to the (I)-CDES-90 reference frame) with standard errors of the mean (1 SE) of 0.006 to 0.011 ‰ (Tables 1 and 2).This translates into analytical temperature uncertainties between 1.5 and 3.8 °C (1 SE).The Δ 47 values were converted into temperatures using the calibration equation of Anderson et al. 19 (Tables 1 and 2), resulting in formation temperatures between 10.8 and 42.5 °C and uncertainties of 2.6 to 4.3 °C which include the uncertainty of the calibration equation of 1.9-2.4°C (95% CL) (Table 1).

Fluid inclusion water isotopes (δ 2 H w, δ 18 O w ) and isotope geothermometry
Of the six samples that were initially selected for water isotope analysis based on FI petrography (containing predominantly primary FIs), only three (ESZ-3, SB-10, and SPA-147) contained sufficient water for stable isotope analysis (0.1 to 0.9 µL/g).Water was released from the FIs by crushing 0.9 to 1.4 g of calcite.In total 18 measurements were performed (4 to 9 replicates per sample; Table S4).Measured δ 18 O w yielded 1 SD between 1.3 and 2.4 ‰, leading to temperature uncertainties of ~ 6 to 14 °C.We therefore calculated δ 18 O w from the measured Table 1.Comparison of temperatures obtained by NA-FIM, Δ 47 and OIT methods.NA-FIM temperatures are reported as standard error of the mean (1 SE) and also account for the overall analytical precision.Δ 47 values are reported relative to (I)-CDES-90.Clumped isotope temperatures were calculated after Anderson et al. 19 and 1 SE errors include the uncertainty of the calibration..Measured and calculated FI oxygen isotope values agree within the 1 SD (Table S4).Given the lower uncertainty of δ 2 H w , we used the calculated δ 18 O w values along with the δ 18 O c values measured on the crushed samples to calculate calcite formation temperatures applying the equation of Daëron et al. 22 .We chose this calibration because it is based on very slow-growing calcite from two subaqueous environments (Devils Hole, USA, and Corchia Cave, Italy), similar to the studied calcite spars.Mean temperatures derived from the replicate measurements are given in Table 1.Uncertainties include the standard deviation of δ 2 H w obtained from replicate measurements (Table S4) as well as the analytical uncertainty of δ 18 O c measurements.For formation temperatures calculated by other equations (e.g., Kim and O'Neil 23 ; Tremaine et al. 24 ) we refer the reader to the Supplementary Information (Table S6).

Stalagmites, calcite spar and low-temperature geothermometry
An earlier attempt to systematically compare methods of low-T calcite geothermometry was reported by Meckler et al. 25 .This study was performed on two stalagmites formed in a limited temperature range of ca.18-24 °C.Deposition of calcite in stalagmites occurs under subaerial conditions and at atmospheric pressure, therefore calcite precipitation is controlled by degassing of CO 2 from a thin water film.The isotopic composition of calcite in such vadose settings may reflect both primary depositional parameters (i.e., δ 18 O of meteoric water, cave air temperature and δ 13 C of the carbonate bedrock and the soil-derived CO 2 dissolved in water), and possible kinetic processes during precipitation (e.g., Rayleigh distillation of the HCO 3 − reservoir during degassing of CO 2 or evaporation 26 ).
Given its depositional setting, stalagmite calcite appears to be an ideal candidate to apply the NA-FIM method (provided that T is higher than 9 °C).Calcite deposition at atmospheric pressure eliminates the need for pressure correction and the measured T h∞ values faithfully reflect the formation T. Dripstone caves, however, are less suitable for the application of isotope-based thermometry (Δ 47 and OIT), as isotopic equilibrium during calcite precipitation cannot be assumed, and must always be ascertained by replication 27 .Meckler et al. 25 .demonstrated that the empirical speleothem-based fractionation equation of Tremaine et al. 24 compensated for an average disequilibrium and thus provided accurate temperature estimates for the two stalagmites, whereas other studies used a cave-specific Δ 47 -thermometer calibration based on modern-day speleothems to correct for disequilibrium isotope fractionation 28,29 .
In contrast to stalagmites, calcite spar forms in phreatic settings, typically at elevated temperatures.The main mechanism controlling the deposition of calcite in such environments is the very slow degassing of CO 2 , caused by slow upwelling (decreasing pressure) and slow cooling of the groundwater 18,30,31 .Slow CO 2 degassing in deep-seated conditions within large groundwater bodies greatly reduces the possibility of kinetic processes and renders their distorting effects on isotopic systematics of the depositing spar negligible.
In most cases, the depth (and, respectively, P) of calcite spar precipitation is not known, and can only be assessed indirectly.From geochemical considerations, precipitation of low-T hydrothermal calcite is unlikely to occur at depths exceeding 300 m (at hydrostatic pressure conditions 30 ).T h values of FIs provide a minimum Table 2. Comparison of Δ 47 temperatures obtained in the laboratories of Heidelberg and Debrecen.Clumped isotope temperatures were calculated after Anderson et al. 19 .Δ 47 values measured in Heidelberg are reported relative to CDES-90 (carbon dioxide equilibrium scale at 90°C), while data measured in Debrecen are reported relative to I-CDES.The ∆ 47 values of the two laboratories were combined by calculating an error-weighted mean of the (I)-CDES-90 values for each sample.The ∆ 47 uncertainty of the combined data is given as standard error (1 SE), which includes the temperature uncertainty of the calibration line of Anderson et al. 19 .www.nature.com/scientificreports/estimate of the temperature of formation, and a pressure correction is required to compensate for the elevated P at the site of calcite precipitation.All our samples are from competent carbonate rocks and therefore we assume a hydrostatic pressure gradient (~ 10 MPa/km).As the pressure correction is ca. 1 °C/MPa, the T h of calcite formed in deep phreatic conditions may underestimate the formation T by up to ca. 3 °C.In summary, calcite spar is an excellent candidate for comparing isotope-based thermometry (Δ 47 and OIT) and NA-FIM, with a small bias towards lower temperatures in the latter method.

Temperature of formation and calcite crystal morphology
The calcite crystal morphology reflects the environmental conditions and the composition of the water.Although the controlling parameters are numerous (T, pCO 2 , trace elements, etc.), empirical studies of natural systems revealed a more or less systematic evolution of crystal morphology [32][33][34] .Calcite crystals forming in ambienttemperature caves have a characteristic rhombohedral (with dominant steep rhombohedra) and, less commonly, scalenohedral morphologies 35 .Among our samples, we observed steep rhombohedral, blunt rhombohedral and scalenohedral crystal morphologies (Table S1).The steep rhombohedral calcites yielded the lowermost temperatures of formation (NA-FIM; 11-13 °C); crystals with blunt rhombohedral morphologies formed in a relatively wide temperature interval of 12-29 °C; and scalenohedral calcites formed between > 30 °C (Fig. S3).Thus, we propose that the crystal morphology (rhombohedral vs. scalenohedral) may be used to discriminate between lower-and higher-T varieties of calcite spar.This is consistent with data from deep carbonate aquifers 36 .

Comparison of NA-FIM and Δ 47 temperatures
The T h∞ data indicate that the studied calcite samples precipitated between ca.11 and 44 °C.To calculate Δ 47 temperatures we applied the unified regression equation of Anderson et al. 19 .A comparison of the NA-FIM and Δ 47 temperatures is shown in Fig. 2. The regression line has a slope close to unity (0.90), an intercept of 1.04 °C and a SE of 4.7 °C, yielding a 95% confidence interval of ± 9.4 °C.
As discussed above, data obtained using NA-FIM may slightly underestimate temperatures (by < 3 °C) due to (possibly) elevated hydrostatic pressure during spar formation.Δ 47 temperatures, in contrast, are considered as true calcite formation temperatures.Assuming that the Δ 47 temperatures are accurate, they are expected to be equal to or higher than T h∞ .
One sample (NKQ4-3) yielded Δ 47 temperatures significantly higher than T h∞ .Two growth phases were identified in this sample: an early (NKQ4-3-1, core) and a later stage (NKQ4-3-2, rim), with temperature differences between the two methods of 9.8 ± 4.9 °C and 9.3 ± 3.5 °C, respectively (Table 1, Fig. 2).If both temperature estimates are accurate, this difference may be used to estimate the fluid trapping pressure.The 9.8 ± 4.9 °C and 9.3 ± 3.5 °C difference therefore suggests calcite precipitation at a minimum depth of ca.490 m.The scenario  19 ) obtained on the same samples.Black circles show measured T h∞ ; open circles show T h∞ + 3°C (corrected for 300 m of hydrostatic pressure).Red circles mark stalagmite data from Meckler et al. 25 Δ 47 temperatures were re-calculated using the calibration of Anderson et al. 19 .Dashed black line shows regression line; dashed red lines correspond to the 95% probability interval.Errors are shown by transparent boxes (1 SE, Table 1).Samples NKQ4-3-1 and NKQ4-3-2 (in orange) were excluded from the regression.www.nature.com/scientificreports/ of calcite forming at such great depth, however, is unlikely, because calcite deposition is not expected at depths greater than about 300 m 30 .However, calcite spar formation at a depth of ~300 m cannot be ruled out and would be consistent with regional groundwater temperatures (~ 40 °C at 500 m depth 37 ).The similar temperature offset between NA-FIM and Δ 47 -temperatures in the two growth phases of NKQ4-3 may indicate non-equilibrium isotope fractionation or its combination with calcite deposition at a maximum depth of about 300 m.NKQ4-4 represents the next calcite generation in this mineralization sequence, for which the results of the two geothermometry methods agree (Table 1).

Comparison of NA-FIM and OIT temperatures
We applied δ 18 O thermometry to three samples (ESZ-3, SB-10 and SPA-147).The small number of samples is related to two factors: (1) five spars contained secondary fluid inclusions and thus the isotope values measured on FI waters are not representative of the paleowater, and (2) three of the samples did not contain enough water for reliable analyses.Although our assessment of OIT vs. NA-FIM thermometry is based on only three samples, these observations may have important implications for future studies.For these three samples robust estimates of δ 18 O w were obtained by isotopic analysis of FI water (δ 2 H w, δ 18 O w ).Calcite formation temperatures were calculated using the fractionation equation of Daëron et al. 22 (Table S4).A comparison of the NA-FIM, Δ 47 and OIT temperatures is shown in Fig. 3.While temperature estimates obtained by the three methods in general agree for two samples, OIT yielded a significantly higher temperature than the other two methods for sample SPA-147 (Table 1, Fig. 3).Based on the relationship of Daëron et al. 22 and measured Δ 47 temperatures, we obtained a δ 18 O value of -14.4 ± 0.6 ‰ for the mineral-forming water, which corresponds to the measured and estimated δ 18 O w using the FI isotope data (Table S4).Therefore, we propose that the δ 18 O w may have remained rather constant over time, and the increase in δ 18 O c across the calcite crystal (Fig. S2) may indicate a change in the temperature of the paleowater.The ~ 1.7 ‰ difference in δ 18 O between the bulk calcite crushed for OIT and the subsample measured for Δ 47 thermometry could account for the higher T yielded by OIT.

Assessing the precision and accuracy of temperature reconstructions
As discussed above, the NA-FIM method offers an internal quality check.As long as the measurements are done on FIAs rather than on individual inclusions, the consistency and reliability of the thermometric results is ascertained by the tightness of the T h distribution.In FI research, a result is deemed consistent if 90% of the T h measurements made on individual FIAs fall within a 10 °C-interval 7 .On the basis of this criterion, the data in this study are highly consistent, with some sets of measurements (T h∞ ) plotting within a 3-4 °C interval (Fig. 1).Such tight distributions essentially rule out any post-formational alteration of the initial volumes of FIs, either due to natural processes or sample preparation.
Temperatures derived by the NA-FIM and Δ 47 methods define a linear relationship, justifying the application of linear regression analysis.For the evaluated Δ 47 temperature calibration equation 19 , we obtained R 2 = 0.91 (p-value < 0.001), if all data are considered.If NKQ4-3-1 and NKQ4-3-2 are treated as outliers, the calculated regression line has an R 2 = 0.95 (p-value < 0.001).We therefore conclude that only 5% of the Δ 47 temperatures    www.nature.com/scientificreports/are inconsistent with the NA-FIM temperatures.The standard error of the regression is ± 3.3 °C leading to a 95% confidence interval of ± 6.6 °C.).
The observed deviations between NA-FIM and Δ 47 temperatures do not show a systematic pattern.A similar non-systematic pattern was shown by an earlier study 4 that focused on calcite cements formed at higher T (60-100 °C); however, FIM for these samples yielded much larger uncertainties (9-20 °C).For the spars examined in this study, these variations may be due to several processes that affect the Δ 47 of calcite, including 13 C- 18 O bond reordering during burial, and non-equilibrium isotope effects during mineral formation.Although 13 C- 18 O bond reordering through solid-state diffusion 39 may alter the initial Δ 47 signal, isotope exchange in carbonate minerals requires T > ca. 100 °C and > 10 6 -10 8 years 40 .As our samples formed below ~ 50 °C and experienced no later burial, the initial Δ 47 values are regarded as pristine.
As noted above, one of the samples (NKQ4-3) may have been affected by non-equilibrium isotopic fractionation (e.g., rapid mineral precipitation and/or fast CO 2 degassing) leading to temperature biases that would manifest in Δ 47 temperatures being significantly higher than corresponding NA-FIM temperatures.We consider fast crystal growth highly unlikely as a potential cause of Δ 47 disequilibrium given the large size of the spars (several cm) and their well-developed euhedral morphology (Sample selection in the Supplementary Information).In addition, no evidence of high supersaturation (e.g., instances of crystal nucleation; competitive growth of multiple crystals) was detected by optical microscopy.Dreybrodt 41 suggested that in subaqueous settings, nonequilibrium isotope effects driven by Rayleigh distillation of the dissolved HCO 3 − reservoir during degassing of CO 2 and calcite precipitation can be excluded.Rayleigh distillation would lead to an increase in δ 18 O c and a decrease in Δ 47, whereby a 1‰ shift in δ 18 O c would correspond to ~ − 0.02‰ in Δ 47 42,43 .Thus, we propose that processes other than CO 2 degassing and fast crystal growth likely drove the measured disequilibrium Δ 47 effects.
Although absolute temperatures differ between NA-FIM and clumped isotope thermometry in the two growth phases of sample NKQ4-3, a ca. 12 °C decrease is indicated by both NA-FIM data (from 32.7 ± 0.6 to 20.4 ± 0.5 °C) and Δ 47 temperatures (from 42.5 ± 4.3 to 29.7 ± 3.0 °C, Table 1, Fig. 2 and Fig. S4a).Furthermore, δ 18 O c increases from -11.9 to -9.4‰ from the core to the rim of this crystal (Fig. S2).This 2.5‰ rise also suggests a ca.11 °C temperature increase 22 , assuming that the δ 18 O value of the paleowater remained unchanged, as suggested by the calculated δ 18 O w values (Fig. S4b).

Strengths and weaknesses of the three geothermometry methods for low-T calcite spar
The successful application of each of the three techniques (NA-FIM, Δ 47 -thermometry and OIT) depends on the sample material.These techniques are based on two features, the calcite matrix (Δ 47 -thermometry) and FIs therein (NA-FIM), and on the combination of these two (OIT).
NA-FIM appears to be the most robust and precise of the three methods for studying low-T calcite spar.It yields the smallest uncertainty (between 0.5 and 1.6 °C, Table 1) and thus allows for the reconstruction of finescale (< 3 °C) T changes (e.g., NKQ4-3 samples, Fig. S4).Furthermore, this method has a built-in quality check, defined by the tightness of T h distributions.
Samples to be analyzed by NA-FIM must (i) contain primary FIs, (ii) the FIs must be sufficiently large to observe the phase transitions during microthermometric analyses, and (iii) the samples must have formed above 9 °C.Another caveat that needs to be considered is that FIM, when applied to calcite spar, provides minimum estimates of formation T only.For minerals formed at significant depth the pressure correction may reach several degrees.Since in most cases the depth of mineral formation is not well known, the pressure correction cannot be performed with high accuracy.Importantly, this constraint is not relevant for speleothems, which form under atmospheric pressure conditions.
Unlike NA-FIM, Δ 47 -thermometry can be performed on all calcite samples and it is applicable to T as low as 0°C 44 .Although this method can also detect T changes of less than 3-5 °C, individual measurements have larger analytical uncertainties when compared to NA-FIM.In our study of slow-growing calcite spar, 1 SE ranged from 1.5 to 3.8 °C (excluding the T uncertainty of the Δ 47 -T calibration after Anderson et al. 19 , Table 2), which may be further reduced by improved measurement statistics (e.g. 25,38).Comparable uncertainties were obtained in a previous study 3 for similar calcite spars formed at 10-20 °C and at 120-130 °C.
Finally, our study indicates that in addition to uncertainties discussed above, the ∆ 47 temperature deviate from NA-FIM temperature in a non-systematic way.The standard error of regression for the data is 3.3 °C, resulting in a 95% confidence interval of ± 6.6 °C.
The application of the OIT is rather challenging for calcite spar.Like the ∆ 47 method, OIT is based on the assumption that the calcite was formed in isotopic equilibrium with the paleowater.For samples formed in deep phreatic settings such as calcite spar, this assumption appears justifiable.It may be less so for calcite of vadose speleothems or travertine, whose formation is commonly associated with relatively fast degassing of CO 2 .In most cases, the question of whether a given sample was deposited in isotopic equilibrium remains unanswered, adding to the uncertainty of T estimates.
Independent knowledge of the δ 18 O value of the paleowater is crucial for the application of OIT.The most accurate approach is to determine this parameter by analysing the isotopic composition of FIs.However, this is only feasible for samples containing exclusively primary FIs.This is relatively common in speleothem calcite 25,48,49 , but is rarely the case for calcite spar.For example, only six out of 13 of our samples fulfilled this criterion, and only three samples contained enough water for reliable analyses.www.nature.com/scientificreports/Further complication arises from the possibility of oxygen isotopic exchange between FI water and the host calcite.Such exchange is particularly likely if the mineral formed at T that are higher than the modern-day ambient T. In such situations, δ 18 O w must be evaluated based on δ 2 H w (which is not affected by isotopic exchange with the calcite host).This approach, however, introduces additional uncertainty because the relationship between δ 2 H w and δ 18 O w at a time of calcite formation must be assumed.
Finally, our limited data set shows a good agreement between OIT, NA-FIM and Δ 47 temperatures for two samples (Fig. 3).In contrast, the third sample (SPA-147) shows a discrepancy between OIT and the other two geothermometry methods.This possibly arises from the much larger sample size required for OIT, resulting in an averaging of the formation T gradient captured by this sample (Fig. S1).
In summary, for future geothermometry work using low-T calcite spar, we recommend the use of NA-FIM if the calcite contains primary FIAs.Although this method is labour-intense, it provides the most precise and accurate T estimates of the three methods and it is insensitive to non-equilibrium isotopic fractionation.Furthermore, fine-scale (< 3 °C) T changes can be detected with NA-FIM, which is still challenging for Δ 47 -thermometry, given the larger analytical uncertainties of this method.Our study demonstrates that ∆ 47 -thermometry provides reliable T estimates for calcite spars formed between 9 and 50 °C.Yet, these natural calcites might be affected by kinetic isotope fractionation, potentially leading to formation T uncertainties that may exceed 1 SE.Combining ∆ 47 with high-precision ∆ 48 measurements 44 and continuing efforts in improving interlaboratory comparability are promising developments of future applications of low-T geothermometry using calcite spar.

Sample preparation
Calcite spar samples were sectioned using a low-speed precision saw (IsoMet, Buehler).Doubly-polished 150-300 µm-thick sections were prepared at the University of Innsbruck for FI petrography and microthermometry.The positions of FIAs were marked both on the thick sections using a pen and on the original billets, to enable subsequent sampling for clumped isotope analysis.Based on petrographic observations, 13 FIA-bearing zones in 11 calcite samples were selected for this study.Two different areas were investigated in samples ESZ-2 and NKQ4-3 to check for potential T changes during the growth history of these crystals.Optical microscopy indicated no petrographic changes in ESZ-2, but distinct growth zones in NKQ4-3 marked by FI-rich areas suggest changing growth conditions.In NKQ4-3 the two studied FIAs are separated by a ca. 1 mm-thin red zone stained by iron oxides.

Nucleation-assisted fluid-inclusion microthermometry (NA-FIM)
NA-FIM on single-phase FIs was carried out at the Department of Earth Science, University of Bergen.The analyses were performed using a Linkam THSMG 600 heating/freezing stage mounted on an Olympus BX53 microscope.The microscope is connected to an amplified Ti:sapphire femtosecond laser (CPA-2101, Clark-MXR, Inc.).The 775 nm laser beam is coupled into the microscope light path via a dual port intermediate tube equipped with a short-pass dichroic mirror and focused on the sample through a 100 × long-working-distance objective (Olympus LMPLFLN).Bubble nucleation was induced in the metastable liquid state of the inclusions by means of a single laser pulse 9 .The setup allows for repeated and precise T h measurements of initially single-phase FIs.T h was measured for each individual inclusion at least twice.The reproducibility (precision) is typically within 0.1 °C (± 0.05 °C).In addition, vapor bubble radii were measured at known T in order to correct for the effect of surface tension on liquid-vapor homogenization using the thermodynamic model proposed by Marti et al. 10 The overall analytical precision of T h for individual inclusions is in the range of ± 0.2 to 0.4 °C.Uncertainties of NA-FIM temperatures are given as standard error (1 SE) and also include analytical uncertainties.
Freezing experiments were performed at the University of Innsbruck.The measurements were carried out on a Linkam THMS600 heating-freezing stage mounted on an Olympus BX41 microscope.Fls were cooled down to −40 °C and then slowly heated to detect ice melting temperatures.

Clumped isotope analyses of calcite
Clumped isotope analyses were carried out at the University of Heidelberg.In order to obtain a larger number of replicates, all samples except one (FEC-1) were re-analysed at the Isotope Climatology and Environmental Research Centre (ICER), Institute for Nuclear Research (ATOMKI), Debrecen (Tables 1 and 2).While few of the repeats were performed on the same powder samples on which the first set of measurements was obtained, most samples had to be re-drilled.Spar FEC-1 was not re-analysed as there was only very little material left.Heidelberg 10-12 mg aliquots of calcite powder were obtained from the same parts of the samples where the FIs were studied.Each sample was split into several aliquots, and samples weighing 2-3 mg were used per measurement round.All aliquots were subject to identical preparation and measurement procedures.Clumped isotope analyses were carried out on a MAT 253 Plus isotope ratio mass spectrometer (Thermo Fisher Scientific) following the method described in Kluge et al. 50and Weise and Kluge 51 .All samples were reacted with phosphoric acid at 90 °C for 10 min in individual reaction vessels to produce CO 2 for isotopic analysis.The CO 2 was continuously collected during the reaction and cryogenically cleaned afterwards with an additional passage through a Porapak filled column at −35 °C.Each mass spectrometric analysis of the cleaned CO 2 gas consisted of eight acquisitions with ten cycles per acquisition and included a background measurement for water vapour and air remainders 51 .Simultaneously to the m/z 44-49 readings a baseline signal on m/z 47.5 was recorded and used for pressurebaseline correction that affects m/z 47 51 .

Figure 2 .
Figure 2. Comparison of NA-FIM and Δ 47 temperatures (using the calibration by Anderson et al.19 ) obtained on the same samples.Black circles show measured T h∞ ; open circles show T h∞ + 3°C (corrected for 300 m of hydrostatic pressure).Red circles mark stalagmite data from Meckler et al.25 Δ 47 temperatures were re-calculated using the calibration of Anderson et al.19 .Dashed black line shows regression line; dashed red lines correspond to the 95% probability interval.Errors are shown by transparent boxes (1 SE, Table1).Samples NKQ4-3-1 and NKQ4-3-2 (in orange) were excluded from the regression.

Figure 1 .
Bubble-size corrected homogenization temperatures (T h∞ ) of initially single-phase fluid inclusions in calcite spar samples (bin size 1 °C).Grey shaded areas show the probability density distribution of the Δ 47 data (± 1 SE).